\xiti
\begin{enhancedline}

\begin{xiaotis}

\xiaoti{$a$ 是怎样的实数时，下列各式在实数范围内有意义？\\
    $\sqrt{a - 2}$；\quad  $\sqrt{2 - a}$；\quad $\sqrt{a + 2}$；\quad $\sqrt{(a - 2)^2}$。
}

\xiaoti{把下列各式写成平方差的形式，再分解因式：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={9em, colsep=0pt}}
        \xxt{$x^2 - 9$；} & \xxt{$a^2 - 3$；} & \xxt{$4a^2 - 7$；} & \xxt{$16b^2 - 11$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={12em, colsep=0pt}}
        \xxt{$(\sqrt{11})^2$；} & \xxt{$\sqrt{(-13)^2}$；}                       & \xxt{$-\sqrt{(5 \times 6)^2}$；} \\
        \xxt{$\sqrt{a^6}$；}    & \xxt{$\left(-7\sqrt{\dfrac{2}{7}}\right)^2$；} & \xxt{$\sqrt{(x + 5)^2}$；}
    \end{tblr}

    \begin{tblr}{columns={colsep=0pt}, column{1}={18em}}
        \xxt{$\sqrt{x^2 - 2x + 1} \quad (x \geqslant 1)$；} & \xxt{$(\sqrt{x - y})^2 \quad (x \geqslant y)$；} \\
        \xxt{$\sqrt{x^2 - 4x + 4} \quad (x < 2)$；}         & \xxt{$x + y + \sqrt{x^2 - 2xy + y^2} \quad (x < y)$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={12em, colsep=0pt}}
        \xxt{$\sqrt{9 \times 25}$；}  & \xxt{$\sqrt{36 \times 256}$；} & \xxt{$\sqrt{25 \times 81 \times 289}$；} \\
        \xxt{$\sqrt{13^2 - 12^2}$；}  & \xxt{$\sqrt{65^2 - 16^2}$；}   & \xxt{$\sqrt{9a^2}$；} \\
        \xxt{$\sqrt{(x + y)^2c^2}$；} & \SetCell[c=2]{l}{\xxt{$\sqrt{(a + b)^2 (a - b)^2} \quad (a < b)$。}} &
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{化简：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}, column{2-3}={12em}}
        \xxt{$\sqrt{5^6 \times 3}$；}  & \xxt{$\sqrt{242 \times 49}$；} & \xxt{$\sqrt{(-32) (-15)}$；} \\
        \xxt{$\sqrt{4x^3}$；}          & \xxt{$\sqrt{7a^4}$；}          & \xxt{$\sqrt{5a(x + a)^2}$；} \\
        \xxt{$\sqrt{8(a + b)^4 (c - d)^4}$；}  &  \SetCell[c=2]{l}{\xxt{$\sqrt{a^{2n}} \quad (n \text{是正整数})$。}} &
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{把下列各式中根号外面的因式适当改变后移到根号里面：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={12em, colsep=0pt}}
        \xxt{$2\sqrt{6}$；}   & \xxt{$-5\sqrt{7}$；}            & \xxt{$4\sqrt{\dfrac{1}{2}}$；} \\
        \xxt{$-2a\sqrt{b}$；} & \xxt{$\dfrac{2}{3}\sqrt{3}$；}  & \xxt{$ab\sqrt{\dfrac{1}{a} + \dfrac{1}{b}}$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={colsep=0pt}, column{1}={12em}, rows={rowsep=0.5em}}
        \xxt{$\sqrt{\dfrac{9}{49}}$；}   & \xxt{$\sqrt{2\dfrac{34}{81}}$；}    & \xxt{$\sqrt{\dfrac{0.16}{0.0225}}$；} \\
        \xxt{$\sqrt{\dfrac{0.01 \times 64}{0.36 \times 324}}$；}   & \xxt{$\sqrt{\dfrac{27}{100}}$；}    & \xxt{$\sqrt{\dfrac{25y^4}{121x^6}}$；} \\
        \xxt{$\sqrt{\dfrac{18a^2}{4b^2}}$；} & \xxt{$\sqrt{\left(1\dfrac{1}{25}\right)^2 - \left(\dfrac{2}{5}\right)^2}$；}  & \xxt{$\sqrt{130^2 - 66^2}$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{化去下列各式中根号内的分母：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={12em, colsep=0pt}}
        \xxt{$\sqrt{\dfrac{1}{6}}$；} & \xxt{$\sqrt{2\dfrac{3}{11}}$；} & \xxt{$\sqrt{\dfrac{127}{32}}$；}
    \end{tblr}

    \begin{tblr}{columns={18em, colsep=0pt}, rows={rowsep=0.5em}}
        \xxt{$8\sqrt{\dfrac{3}{128}}$；} & \xxt{$\sqrt{\dfrac{n^3}{9m}}$；} \\
        \xxt{$a\sqrt{\dfrac{b}{a^5}}$；} &  \xxt{$\sqrt{\dfrac{7(a - b)}{27(a + b)}} \quad (a > b)$；} \\
        \xxt{$a\sqrt{\dfrac{1}{a^2} - \dfrac{1}{b^2}} \quad (a < b)$；} & \xxt{$\sqrt{\dfrac{a + b}{(a - b)^2}} \quad (a < b)$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{把下列各式化成最简二次根式：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={12em, colsep=0pt}}
        \xxt{$\sqrt{72}$；} & \xxt{$6\sqrt{\dfrac{1}{8}}$；} & \xxt{$10\sqrt{1\dfrac{4}{5}}$；}
    \end{tblr}

    \begin{tblr}{columns={colsep=0pt}, column{1}={18em}, rows={rowsep=0.5em}}
        \xxt{$\sqrt{(-8)^2 - 4 \times (-4)}$；} & \xxt{$\sqrt{\left(3\dfrac{1}{2}\right)^2 + \left(\dfrac{1}{2}\right)^2}$；} \\
        \xxt{$\sqrt{\dfrac{x}{y}}$；} &  \xxt{$\sqrt{25m^3 + 50m^2}$；} \\
        \xxt{$\dfrac{2a^2}{3b}\sqrt{\dfrac{b^3}{a^4} - \dfrac{b^2}{a^4}} \quad (b > 1)$；} & \xxt{$\dfrac{a}{a - 2b}\sqrt{\dfrac{a^2b - 4ab^2 + 4b^3}{a}} \quad (a < 2b)$。}
    \end{tblr}

\end{xiaoxiaotis}


\xiaoti{求当 $a = 1$， $b = 10$， $c = -15$ 时，代数式 $\dfrac{-b + \sqrt{b^2 - 4ac}}{2a}$ 的值（用最简二次根式表示）。}

\xiaoti{求当 $a = 2$， $b = -8$， $c = 5$ 时，代数式 $\dfrac{-b - \sqrt{b^2 -4ac}}{2a}$ 的值（用最简二次根式表示）。}

\xiaoti{下列二次根式中，哪些是同类二次根式？ \\
    $\sqrt{8}$\nsep $\sqrt{20}$\nsep $-\sqrt{\dfrac{5}{16}}$\nsep $\sqrt{\dfrac{1}{18}}$\nsep $3\sqrt{\dfrac{4}{5}}$\nsep $-\sqrt{121a^3}$\nsep
    $a\sqrt{\dfrac{1}{a}}$\nsep $2\sqrt{a^3b^3c}$\nsep \\
    $3\sqrt{a^3bc^3}$\nsep $4\sqrt{\dfrac{c}{ab}}$\nsep  $\sqrt{\dfrac{1}{mn - np}} \quad (m > p)$\nsep
    $\sqrt{\dfrac{n^3}{m - p}} \quad (m > p)$。
}


\xiaoti{合并下列各式中的同类二次根式：}
\begin{xiaoxiaotis}

    \xxt{$\sqrt{2} + \sqrt{3} + 3\sqrt{2} - \dfrac{\sqrt{3}}{3} - \dfrac{\sqrt{2}}{2}$；}

    \xxt{$\sqrt{125} + 3\sqrt{\dfrac{2}{27}} - 4\sqrt{216} + 3\sqrt{\dfrac{1}{5}}$；}

    \xxt{$5\sqrt{xy} - 7\sqrt{x} - 3\sqrt{yx} + 4\sqrt{x}$；}

    \xxt{$2a\sqrt{3ab^2} - \left(\dfrac{b}{5}\sqrt{27a^3} - 2ab\sqrt{\dfrac{3a}{4}}\right)$。}

\end{xiaoxiaotis}
\end{xiaotis}
\end{enhancedline}
